Influence of randomness and retardation on the FMR-linewidth

Abstract

The theory predicts that the spin-wave lifetime τ_L and the linewidth of ferromagnetic resonance ΔB can be governed by random fields and spatial memory. To that aim the effective field around which the magnetic moments perform a precession is superimposed by a stochastic time dependent magnetic field with finite correlation time. The magnetization dynamics is altered by inclusion of a spatial memory effect monitoring a non-local interaction of size ξ. The underlying Landau–Lifshitz–Gilbert equation (LLG) is modified accordingly. The stochastic LLG is equivalent to a Fokker–Planck equation which enables to calculate the mean values of the magnetization vector. Within the spin-wave approximation we present an analytical solution for the excitation energy and its damping. The lifetime and the linewidth are analyzed depending on the strength of the random field D and its correlation time τ_c as well as the retardation strength Γ₀ and the size ξ. Whereas τ_L decreases with increasing D, retardation strength Γ₀ and τ_c, the lifetime is enhanced for growing width ξ of the spatial retardation kernel. In the same manner we calculate the experimentally measurable linewidth ΔB is increased strongly when the correlation time τ_c ranges in the nanosecond interval.